Australia's 2007 elections – IRV pathologies undermine its success

IRV advocate
Rob Richie recently hailed the Australian house
elections (held 24 November 2007) as a
"big success" for Instant Runoff Voting (IRV).
These elections threw out both Prime Minister John W. Howard
and his party, the NatLibs, enthroning
Kevin Rudd and giving his Labour Party majority control.

But was this really a big success for IRV? We'll examine that here using data from
the
Australian Electoral Commission
web site.
(Warning: All this is based on data we got from the AEC
on 30 November 2007, which was not in final form. However, it turned out
the same seat counts ultimately arose, in the final say, as we tabulated.)
The conclusions of that examination are as follows:

If Australian house elections had been held with plain
plurality
voting rather than
IRV
then (assuming every voter would have voted for the same
candidate they top-ranked with IRV)
the results of 9 of the 150 House races would have changed.
In all 9 cases, plurality voting would have elected the NatLib candidate instead
of the Labour candidate who actually won with IRV.
More realistically, with plurality probably some third-party voters would have been more-afraid
to vote third party and would have voted for the top-two party candidates. If so, then
fewer than "9" races would alter (perhaps only 7 or 8?).
That would decrease the
importance of IRV in one way (fewer results changed)
but in another sense (improved voter honesty) would increase it back.

Labour and Rudd still would have won majority control with plain plurality voting, just
a smaller majority (77 out of 150 seats, versus what they got with IRV, which was 85 out of 150).

In view of this, we agree with Rob Richie that these elections were
at least a "success"
(albeit perhaps not a "big success")
for IRV.
But we contend approval and range voting would have been an even bigger success, as we'll
now explain.

If Australia had employed
approval,
range,
or
Condorcet
voting instead of IRV, then we believe the same result would have happened,
i.e. exactly the same 9 races
would have swung toward Labour – or perhaps only 7 or 8 with range and approval if
the third-party voters did not approve Labour enough or score it highly enough;
and also the Greens
might have won some races with Range and/or Approval –
but either way
then range & approval would arguably have made a better call than IRV in those cases.

All 9 IRV-swinging races displayed a pathology called "participation failure"
or "no-show paradox." That is, in every case, adding some number of extra
Green>Labour>NatLib voters, would have caused the IRV winner to become NatLib.
That is bad, because:

These extra voters, by voting honestly, would have made the election result worse in their view.

They would have been better off not voting at all (as, in fact, they didn't).

They also would have been better off voting dishonestly; and with these extra Green voters,
some of the Labour voters also would have been better off voting dishonestly.

All 9 losing Natlib candidates have the following valid gripe,
enabling them to attack the legitimacy of IRV:

I lost to Labour with IRV,

But
if extra voters, all of whom ranked me dead last and preferred Labour over me,
entered the picture, then I would have won,

So, since I would have won and
defeated Labour even with this handicap, why the heck did I lose without the handicap?
∴
My defeat was bogus or the election system (IRV) is bogus, or both.

But that whole conclusion and gripe can be avoided, but the
way out involves admitting that there
was a different pathology ("failure to elect Condorcet winner")
which occurred even more frequently.
In each case where this alternate pathology occurred, the
Green loser would have the following valid gripe,
enabling them to attack the legitimacy of IRV:

I would have defeated the Labour candidate if it had been just me versus him.

I also would have defeated the NatLib if it had been just me versus him.

So why did they win and not me?!

∴ This IRV election system and my defeat are both bogus!

Note: there is a 2-way choice here – at least one of these two pathologies (and hence gripes) is
valid in each election, but the incomplete data released by the AEC is insufficient to tell which. I suspect,
however, that the second problem (the Green gripe) is the one that is correct in the vast majority of cases.

Approval and Range cannot exhibit the first sort of pathology and
probably did not exhibit the latter either;
hence apparently
no candidate in
any of the 150
races would have had any such
valid gripe enabling attacking the legitimacy of
range & approval voting.

The myth that IRV pathologies are "extremely rare" is totally refuted.
The claim that IRV improved on plain plurality voting is undermined because
the two systems delivered exactly the same winners in every case, except for
cases in which the legitimacy of IRV can validly be questioned.

Australia is still counting and recounting all the close IRV elections
1 week 2 weeks later and
warn that it is not clear that Labour really has 85 seats, etc (those results are subject to
change).
Update 6 Dec 2007: the AEC still
considers
9 of the 150 seats to be
"doubtful," i.e. insufficiently clear who won, 12 days after the election.
Later update:
As of 11 Dec, improvement! Now only 7 seats are unclear, but the AEC is
closing for Xmas holidays so we cannot know any more for quite a while...
Final update:
As of 28 Dec, over 1 month after the (24 Nov) elections,
the AEC now considers the matter finalized and is awarding Labour 83 seats.
The outcomes of our 9 flagged races, did not change.
That is because
IRV is a difficult system to count, and ties and near-ties even between "no hoper"
candidates, can change the winner.
Australia's
numbers
of invalid "spoiled" ballots
were easily large enough to change the winner in many of the 150 races.
(And, incidentally, spoilage rates are
lower with range and approval voting but higher under IRV.)
Approval (or even range) voting are simpler to count and less subject to tie-crises.
They would have been counted sooner with fewer worries, less effort, and less cost, and
could have been counted in precincts leading
to greater transparency and credibility.

Details

Zero house seats were won by 3rd party members (as usual, same
as the preceding Australian election in 2004 and the one before that in 2001).
But a couple of "independents" all of whom were former major-party members,
hold and held seats.

According to one 6 December count,
there was
93%
(another page said
92%; the
figure changes with time and which AEC web page you look at)
turnout for House races out of
13,645,073 enrolled voters
(despite "compulsory" voting which
"should" have yielded 100% turnout);
7% of voters presumably will pay fines.

1054 candidates ran for the 150 house seats which is 7.03 candidates
per seat average.

Every race was contested by at least 3 candidates.

But it appears there were no "genuine" 3-way races, i.e. the 3rd-placer
was always far behind the top 2 in all 150 races, at least reckoned by top-preference votes.
For that reason,
there was no example of a favorite-betrayal or nonmonotonic
IRV race because it was always basically just a 2-man race.

9 "Participation failure" or "Condorcet failure" pathologies

There were by our count exactly 9 races (of the 150 total races)
where the plurality and IRV winners disagreed.
(You can re-examine the 150 races here:
http://vtr.aec.gov.au/HouseDivisionMenu-13745-NAT.htm. We initially counted 8 but
Malcolm MacKerras pointed out there were actually 9 such
races and we have now added the 9th: Bass.)
In all 9 cases, the Labour candidate did not win the "plurality election"
(IRV round #1) but did win the IRV election.
Here are the 9:

Since the Australian Election Commission ignored my request for more data
(and keeps the full IRV results secret, only distributing simplified election summaries which
are not enough information to reconstruct the ballots)
we are forced to analyse these elections somewhat simplistically.
So let us disregard the other candidates in 4th, 5th, etc place
and assume Green voters prefer Labour over NatLib, while Labour voters do not,
on average, have an especially noticeable Green-over-Natlib preference, i.e.
either would prefer NatLibs or would split about 50-50.
(Note: every other party was well behind the Greens so these assumptions are plausibly OK.)

How realistic are those assumptions, and how much does it matter?
It is definitely correct that a big majority among Greens prefered Labour over the NatLibs;
this is evident both from party stances and more importantly
from the elections themselves, which involved many cases where Green vote-transfers
made the Labour candidate win.
However it is not at all clear that the Labour voters
were neutral, or NatLib-favoring, about NatLib versus Green. There is no way to tell
how the Labour voters ranked the others from the AEC's simplified election summaries,
but we can say that the Labour Party's
pre-made "above the line" vote ranked the
Greens #2 and the NatLibs
second-to-last, which at least suggests Labour voters prefered Greens>NatLibs.
We are nevertheless going to proceed under this
assumption to see what consequences would follow.
Then later, we shall reconsider
what happens if we drop this assumption in favor of the opposite view that
they prefer Green>NatLib.
Actually we shall consider 3 cases:
[c1] the Labour voters prefer Green>NatLib, [c2] prefer NatLib>Green, or [c3] do not care.
In all 3 cases we will see there had to be a pathology in the election, it is just
that we do not always find the same pathology.
We shall begin with cases c2 & c3 now, and
the "reconsideration" will later handle c1
[which is the one I consider most likely to be actually correct].
We proceed:

[c2 and c3]:All nine of
these examples are pathological in the sense that
if we add an appropriate number
(respectively
30200, 33700, 23100, 26500,
23200, 26200, 30100, 17050, and 15000)
of extra Green>Labour>NatLib voters, then those voters, by casting their
honest vote, would cause the result to worsen (their
most-hated NatLib would win in both cases).
In other words we have a "participation failure" or "no-show paradox" or "spoiler"
scenario (all 9 examples have the same structure and all 3 of these epithets are
simultaneously valid in every case) where adding
extra identical honest Green votes would worsen the election winner
in the view of these new voters.

These extra Greenies would be better off dishonestly betraying
their favorite by ranking him/her below top (IRV doesn't care
how far below); they also would be better off not voting (which is in
fact what happened).
That's the "paradox."

So the picture is fairly clear based on my hopefully-exhaustive
examination of all 150 Australian 2007 House races.
Exactly two things happened:

They disagree – but in 9 out of 9 cases where that happened,
there was a "participation failure" paradox/pathology allowing the defeated NatLib a valid
gripe against the legitimacy of both his defeat and the IRV voting system.

Reconsideration –
you can wriggle out of that, but then... meet "Condorcet-failure"!

If the Labour voters all preferred Green>NatLib, then our analysis
above finding
"participation failure" pathology in all 9 IRV-swung elections, is invalidated.
However, we warn IRV-proponents not to be relieved about that. That's because
this new opposed assumption doesn't "save" them so much as
"throw them out of the frying pan into the fire."

Suppose all the Labour, NatLib, and Green voters indeed voted this way.
In that case, Green was the "Condorcet winner," i.e. would
have beaten both rivals in a head-to-head contest, in every race
in which neither the Labour or NatLib won an outright majority – i.e. in
all 9 of the IRV-swung races, plus plausibly a lot more races too.

In all these races, IRV refused to elect that Condorcet winner!
The Green candidate would have had the very legitimate gripe
"I would have defeated every rival head-to-head, so I should have won"!
That's arguably an even worse "pathology" being exhibited by IRV, and
whether or not it was "worse," it definitely occurred more often.